Theorems · Theorem · sequences and series
multipliable_norm_one_add_of_summable_norm
∀ {ι : Type u_1} {R : Type u_2} [inst : NormedCommRing R] [NormOneClass R] {f : ι → R},
(Summable fun i => ‖f i‖) → Multipliable fun i => ‖1 + f i‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedCommRingNormOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- absproof · cited by 1,814
- add_commproof · cited by 1,535
- Summablestatement and proof · cited by 778
- SummationFilterproof · cited by 607
- sub_add_cancelproof · cited by 344
- NormedCommRingstatement and proof · cited by 218
- Multipliablestatement and proof · cited by 213
- add_sub_cancel_leftproof · cited by 198
- NormOneClass.norm_oneproof · cited by 148
Cited by1
Results whose statement or proof uses this declaration.
- multipliable_one_add_of_summableproof · cited by 4